0
$\begingroup$

In the book Gravitational waves vol 1 by Maggiore page 17 it is argued that the coordinate position of a test mass does not change in the TT-frame if the test particle was at rest.

I understand the steps but I don't understand why we can assume that the test mass was at rest in the TT-frame? I think this can only be realized for a GW burst and not for a continuous GW? The particle is at rest before the GW hits the particle and then even when the GW hits the particle remains at rest. The assumption that the particle is at rest would not work if the GW is a continuous wave of a stochastic GW background. Do I understand this correctly?

Improve this question
$\endgroup$
2
  • $\begingroup$ You should specify which book in the question in addition to linking to it, to protect against link rot $\endgroup$
    – Paul T.
    Commented Aug 4, 2021 at 22:32
  • $\begingroup$ Done. Thanks for pointing this out $\endgroup$
    – user255856
    Commented Aug 4, 2021 at 22:38

1 Answer 1

Reset to default
0
$\begingroup$

the coordinate position of a test mass does not change in the TT-frame if the test particle was at rest

The test mass being at rest in the TT frame is an assumption. The conclusion is only valid under that condition. If the test mass were moving in the TT frame, it would continue moving as the GWs passed. The test mass's coordinate velocity would likely change due to the GWs (depending on polarization and direction of motion and the like).

The question seems to be: is this a realistic assumption about the universe?

The thing you are worrying about seems to be that if the GWs existed far into the past, then the test mass must have been at rest in the TT frame far into the past too. It must not have interacted with anything else either (GW calculations typically assume a small perturbation on a vacuum, Minkowski spacetime).

Whether these are valid assumptions has to do with the relative scales of the physical effects. For short duration transient GWs, we can assume the test masses in a GW detector like LIGO are approximately in free fall and approximately at rest in the TT frame. The test masses are not in true free fall, nor are they at rest. The motion of the Earth is slow compared to the scale of the GWs, so it doesn't matter so much. For a long lived, continuous GW source, the data analysis has to take into account the motion of the detector (and the source). The introductory "Chapter 1" presentation will have to be modified to deal with those kinds of sources.

If you want to think about a stochastic background of GWs, it helps to work out the idealized case first. Imagine some test masses at rest in the TT frame and figure out what happens. If you want to build a GW detector and analyze its data, you will have to worry about some extra complications.

Improve this answer
$\endgroup$
2
  • $\begingroup$ short duration transient GWs: I think I can accept now (and also show mathematically) that for short duration transient GWs the test mass is initally at rest in the TT-frame. What I only intuitively understand is why one can assume that the GW detector is in free fall. For what frequency regimes is this a valid assumption? And how would I show this mathematically? $\endgroup$
    – user255856
    Commented Aug 5, 2021 at 5:59
  • $\begingroup$ stochastic background and other continuous sources: I understand that in this case the assumption for initially at rest in the TT-frame does not hold anymore. Can you recommend a mathematically precise reference for how to deal with this case? For example how can I calculate the movement of the LIGO mirrors in the case of stochastic GWs? $\endgroup$
    – user255856
    Commented Aug 5, 2021 at 6:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.